Question

150.0 grams of an isotope with a half-life of 36.0 hours is present at time zero. How long will it take

Answer 1

Given :

Initial mass , a = 150 gm .

Half time ,

$t_{\dfrac{1}{2}}=36 \ hours$.

Final mass , x = 18.75 gm .

To Find :

The time taken to decay 18.75 gm .

Solution :

We know , time taken is given by :

$t=\dfrac{1}{k}\times ln(\dfrac{a}{a-x})$

Here , k is a constant given by :

$k=\dfrac{0.693}{t_{\dfrac{1}{2}}}\\\\\\k=\dfrac{0.693}{36}$

Putting all given value in above equation :

We get :

$t=\dfrac{36}{0.693}\times ln(\dfrac{150}{150-18.75})\\\\t=6.94\ hours$

Therefore , time taken is 6.94 hours .

Hence , this is the required solution .